The Liapunov Center Theorem for a Class of Equivariant Hamiltonian Systems

Jia Li and Yanling Shi

Abstract and Applied Analysis, 2012, vol. 2012, 1-12

Abstract:

We consider the existence of the periodic solutions in the neighbourhood of equilibria for ð ¶ âˆž equivariant Hamiltonian vector fields. If the equivariant symmetry 𠑆 acts antisymplectically and 𠑆 2 = ð ¼ , we prove that generically purely imaginary eigenvalues are doubly degenerate and the equilibrium is contained in a local two-dimensional flow-invariant manifold, consisting of a one-parameter family of symmetric periodic solutions and two two-dimensional flow-invariant manifolds each containing a one-parameter family of nonsymmetric periodic solutions. The result is a version of Liapunov Center theorem for a class of equivariant Hamiltonian systems.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:530209

DOI: 10.1155/2012/530209

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